A Nonlinear Reduced-Order Model for Electrostatic MEMS

2003 ◽  
Author(s):  
Eihab M. Abdel-Rahman ◽  
Mohammad I. Younis ◽  
Ali H. Nayfeh
Keyword(s):  
Equations Of Motion ◽  
Computational Cost ◽  
Design Tool ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Design Parameters ◽  
Mems Devices ◽  
Order Model ◽  
Reduced Order ◽  
Galerkin Procedure

We present an analytical approach and a reduced-order model (macromodel) to investigate the behavior of electrically actuated microbeam-based MEMS. The macromodel provides an effective and accurate design tool for this class of MEMS devices. The macromodel is obtained by discretizing the distributed-parameter system using a Galerkin procedure into a finite-degree-of-freedom system consisting of ordinary-differential equations in time. The macromodel accounts for moderately large deflections, dynamic loads, and the coupling between the mechanical and electrical forces. It accounts for linear and nonlinear elastic restoring forces and the nonlinear electric forces generated by the capacitors. A new technique is developed to represent the electric force in the equations of motion. The new approach allows the use of few linear-undamped mode shapes of a microbeam in its straight position as basis functions in a Galerkin procedure. The macromodel is validated by comparing its results with experimental results and finiteelement solutions available in the literature. Our approach shows attractive features compared to finite-element softwares used in the literature. It is robust over the whole device operation range up to the instability limit of the device (i.e., pull-in). Moreover, it has low computational cost and allows for an easier understanding of the influence of the various design parameters. As a result, it can be of significant benefit to the development of MEMS design software.

Modal Reduced Order Model for Vision Sensing of IPMC Actuator

2006 ◽  
Vol 326-328 ◽  
pp. 1523-1526
Author(s):  
Il Kweon Oh ◽  
Seong Won Yeom ◽  
Dong Weon Lee
Keyword(s):  
Reduced Order Model ◽  
Mode Shapes ◽  
Computational Time ◽  
Transverse Displacement ◽  
Metal Composite ◽  
Motion Generation ◽  
Order Model ◽  
Lower Mode ◽  
Reduced Order ◽  
Vision Sensing

In order to control the IPMC (Ionic Polymer Metal Composite) actuators, it is necessary to use a vision sensing system and a reduced order model from the vision sensing data. In this study, the MROVS (Modal Reduced Order Vision Sensing) model using the least square method has been developed for implementation of the biomimetic motion generation. The simulated transverse displacement is approximated with a sum of the lower mode shapes of the cantilever beam. The NIPXI 1409 image acquisition board and CCD camera (XC-HR50) are used in the experimental setup. Present results show that the MROVS model can efficiently process the vision sensing of the biomimetic IPMC actuator with cost-effective computational time.

Design of a Kangaroo Inspired Hopping Robot for Unrestricted Locomotion and Controller Development

2019 ◽  
Author(s):  
Austin Curtis ◽  
James Mynderse ◽  
Hamid Vejdani
Keyword(s):  
Frequency Response ◽  
Three Dimensional ◽  
Reduced Order Model ◽  
Design Parameters ◽  
Order Model ◽  
Reduced Order ◽  
Gait Performance ◽  
System Parameters ◽  
Hopping Robot ◽  
The Relationship

Abstract Inspired by the agility and maneuverability of running kangaroos, a prototype robot was developed using a reduced order model to constrain the system. Both passive and active models were used to understand the relationship between system parameters and gait performance. A frequency response experiment was performed on the prototype to quantify the relationship between design parameters and system responses. Additionally, preliminary tail controllers were tested. Based on the results of the initial platform, a new robot was designed and built as a platform for the study of three dimensional hopping.

Accuracies of Reduced Order Models of a Bladed Rotor With Geometric Mistuning

2013 ◽  
Vol 136 (7) ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Natural Frequencies ◽  
Domain Analysis ◽  
Forced Response ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Model Based ◽  
Bladed Rotor

The results from a reduced order model based on frequency mistuning are compared with those from recently developed modified modal domain analysis (MMDA). For the academic bladed rotor considered in this paper, the frequency mistuning analysis is unable to capture the effects of geometric mistuning, whereas MMDA provides accurate estimates of natural frequencies, mode shapes, and forced response.

A Reduced-Order Model for Evaluating the Effect of Rotational Speed on the Natural Frequencies and Mode Shapes of Blades

2003 ◽  
Vol 125 (3) ◽  
pp. 772-776 ◽  
Author(s):  
P. Marugabandhu ◽  
J. H. Griffin
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Finite Element Analyses ◽  
Order Model ◽  
Reduced Order ◽  
Low Aspect Ratio ◽  
Centrifugal Stiffening ◽  
Fan Blade

A reduced-order model has been developed that can be used to accurately and quickly calculate the changes in the natural frequencies and mode shapes of a blade that are caused by centrifugal stiffening. It has been corroborated by comparisons with finite element analyses of a cantilevered tapered plate and with frequencies from a low aspect ratio fan blade.

Prediction of Geometrically Induced Localization Effects Using a Subset of Nominal System Modes

2019 ◽  
Author(s):  
Thomas Maywald ◽  
Christoph R. Heinrich ◽  
Arnold Kühhorn ◽  
Sven Schrape ◽  
Thomas Backhaus
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Reduced Order Model ◽  
Vibration Measurement ◽  
Mode Shapes ◽  
Compressor Stage ◽  
Order Model ◽  
Reduced Order ◽  
Numerical Predictions

Abstract It is widely known that the vibration characteristics of blade integrated discs can dramatically change in the presence of manufacturing tolerances and wear. In this context, an increasing number of publications discuss the influence of the geometrical variability of blades on phenomena like frequency splitting and mode localization. This contribution is investigating the validity of a stiffness modified reduced order model for predicting the modal parameters of a geometrically mistuned compressor stage. In detail, the natural frequencies and mode shapes, as well as the corresponding mistuning patterns, are experimentally determined for an exemplary rotor. Furthermore, a blue light fringe projector is used to identify the geometrical differences between the actual rotor and the nominal blisk design. With the help of these digitization results, a realistic finite element model of the whole compressor stage is generated. Beyond that, a reduced order model is implemented based on the nominal design intention. Finally, the numerical predictions of the geometrically updated finite element model and the stiffness modified reduced order model are compared to the vibration measurement results. The investigation is completed by pointing out the benefits and limitations of the SNM-approach in the context of geometrically induced mistuning effects.

scholarly journals A Comprehensive CFD Model for Dual-Phase Brass Indirect Extrusion Based on Constitutive Laws: Assessment of Hot-Zone Formation and Failure Prognosis

Metals ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 1043 ◽  
Author(s):  
George Pashos ◽  
George Pantazopoulos ◽  
Ioannis Contopoulos
Keyword(s):  
Stokes Equations ◽  
Metal Flow ◽  
Computational Cost ◽  
Constitutive Laws ◽  
Reduced Order Model ◽  
Preliminary Evaluation ◽  
Order Model ◽  
Zone Formation ◽  
Reduced Order ◽  
Prediction And Prevention

A numerical method for the precise calculation of temperature, velocity and pressure profiles of the α-β brass indirect hot extrusion process is presented. The method solves the Navier–Stokes equations for non-Newtonian liquids with strain-rate and temperature-dependent viscosity that is formulated using established constitutive laws based on the Zener–Hollomon type equation for plastic flow stress. The method can be implemented with standard computational fluid dynamics (CFD) software, has relatively low computational cost, and avoids the numerical artifacts associated with other methods commonly used for such processes. A response surface technique is also implemented, and it is thus possible to build a reduced order model that approximately maps the process with respect to all combinations of its parameters, including the extrusion speed and brass phase constitution. The reduced order model can be a very useful tool for production, because it instantaneously provides important quantities, such as the average pressure or the temperature of hot-spots that are formed due to the combined effect of die/billet friction and the generation of heat from plastic deformation (adiabatic shear deformation heating). This approach can assist in the preliminary evaluation of the metal flow pattern, and in the prediction and prevention of critical extrusion failures, thus leading to subsequent process and product quality improvements.

Reduced Order Model of Two Coupled MEMS Parallel Cantilever Resonators Under DC and AC Voltage Near Natural Frequency

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Kyle N. Taylor
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Reduced Order Model ◽  
Lagrange Equations ◽  
Order Model ◽  
Reduced Order ◽  
Dc Voltage ◽  
Ground Plate

This paper deals with a system of two coupled parallel identical MEMS cantilever resonators and a ground plate. Alternating Current (AC) and Direct Current (DC) voltages are applied between the first resonator and ground plate, and a DC voltage applied between the resonators. The AC voltage frequency is near natural frequency of the resonators. The electrostatic forces produced by voltages are nonlinear. System equations of motion are obtained using Lagrange equations, then nondimensionalized. The Method of Multiple Scales (MMS) is used to find the steady state frequency response. The Reduced Order Model (ROM) is used to validate MMS results. Matlab is used to find cantilever frequency response of the resonator tip. The DC voltage between resonators is showed to significantly influence the response of the first resonator.

A Reduced Order Model for Evaluating the Effect of Rotational Speed on the Natural Frequencies and Mode Shapes of Blades

2000 ◽  
Author(s):  
P. Marugabandhu ◽  
J. H. Griffin
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Finite Element Analyses ◽  
Order Model ◽  
Reduced Order ◽  
Low Aspect Ratio ◽  
Centrifugal Stiffening ◽  
Fan Blade

A reduced order model has been developed that can be used to accurately and quickly calculate the changes in the natural frequencies and mode shapes of a blade that are caused by centrifugal stiffening. It has been corroborated by comparisons with finite element analyses of a cantilevered tapered plate and with frequencies from a low aspect ratio fan blade.

Forced Vibrations of Slacked Carbon Nanotube Resonators

2010 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis
Keyword(s):  
Perturbation Method ◽  
Multiple Scales ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Beam Model ◽  
Harmonic Load ◽  
Arch Model ◽  
Order Model ◽  
Reduced Order ◽  
Model Equations

In this paper, we present an investigation of the dynamics of electrically actuated carbon nanotubes (CNTs) resonators including the effect of their initial curvature due to fabrication (slack). A nonlinear arch model is used to simulate the motion of the slacked CNT. A reduced-order model using a multimode Galerkin procedure based on the mode shapes of the straight un-actuated CNTs is derived. The reduced-order model equations are integrated numerically with time to reveal the steady-state response of the CNT when actuated by a DC load superimposed to an AC harmonic load. A perturbation method, the method of multiple scales, is used to obtain analytically the forced vibration response due to DC and small AC loads for various slacked CNT. Results of the perturbation method are verified with those obtained by numerically integrating the reduced-order model equations. The effective nonlinearity of the CNT is calculated as function of the slack and the DC load while using a beam model for the CNTs showing a softening dominant behavior.

Computationally Efficient Approaches to Simulate the Dynamics of Microbeams Under Mechanical Shock

2006 ◽  
Author(s):  
Mohammad I. Younis ◽  
Danial Jordy ◽  
James M. Pitarresi
Keyword(s):  
Hybrid Approach ◽  
Computational Cost ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Beam Model ◽  
Mechanical Shock ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order ◽  
Dynamic Loading Conditions

We present computationally efficient models and approaches and utilize them to investigate the dynamics of microbeams under mechanical shock. We explore using a hybrid approach utilizing a beam model combined with the shock spectrum of a spring-mass-damper model. We conclude that this approach is computationally efficient and yields accurate results in both quasi-static and dynamic loading conditions. We utilize a reduced-order model based on the nonlinear Euler-Bernoulli beam model. We demonstrate that this model is capable of capturing accurately the dynamic behavior of microbeams under shock pulses of various amplitudes (low-g and high-g), in various damping conditions, structural boundaries (clamped-clamped and clamped-free), and can capture both linear and nonlinear behavior. We investigate high-g loading cases. We report significant increase in the computational cost of simulations when using traditional nonlinear finite-element models because of the activation of higher-order modes. We demonstrate that the developed reduced-order model can be very efficient in such cases.

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